The present invention relates to a new and distinct variety of peach tree named ‘NJ356’. Our new tree resulted from crossing D90-9 as the seed parent with NJ318 peach tree, as the pollen parent. The new variety differs from seed parent D90-9 (unpatented) in that the new variety has small, non-showy flowers and fruit that ripen in the latter part of the season, while the seed parent has large, showy flowers and fruit that do not ripen during a typical growing season. The new variety differs from pollen parent NJ318 (unpatented) in that the new variety ripens two weeks later and produces well colored, firm fruit, while the pollen parent produces fruit that soften rapidly with a low percentage of blush. In comparison to the commercial peach variety ‘Snow Giant’ (U.S. Plant Pat. No.8,085), the fruit of the new variety has a brighter ground color and matures approximately 10 days earlier. The fruit and leaves of the new variety are also more tolerant to bacterial leaf spot than ‘Snow Giant’. The resulting tree was selected when growing in a cultivated area at a fruit research center in Cream Ridge, N.J.